OFFSET
7,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 7..386
Peter J. Cameron, Daniel Johannsen, Thomas Prellberg, Pascal Schweitzer, Counting Defective Parking Functions, arXiv:0803.0302 [math.CO], 2008.
FORMULA
a(n) ~ (43*exp(1)/720 - 88*exp(2)/15 + 405*exp(3)/8 - 368*exp(4)/3 + 235*exp(5)/2 - 48*exp(6) + 7*exp(7)) * n^(n-1). - Vaclav Kotesovec, Aug 19 2017
MAPLE
S:= (n, k)-> add(binomial(n, i)*k*(k+i)^(i-1)*(n-k-i)^(n-i), i=0..n-k):
a:= n-> S(n, 6)-S(n, 7):
seq(a(n), n=7..23);
MATHEMATICA
S[n_, k_] := Sum[Binomial[n, i]*k*(k+i)^(i-1)*(n-k-i)^(n-i), {i, 0, n-k}];
a[n_] := S[n, 6] - S[n, 7];
Table[a[n], {n, 7, 23}] (* Jean-François Alcover, Feb 24 2019, from Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 18 2017
STATUS
approved